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Calculating long run equilibrium price and output level

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Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by following linear demand function:

P= 200-QA-QB

Where QA and QB are quantities sold by the respective firms and P is the selling price. Total costs functions for the two companies are

TCA = 1,500 + 55QA +Q2A
TCB= 1,200+20QB +2Q2B

Assume that the firms act independently as in cournot model (i.e., each firm assumes that the other firm's output will not change)

a. Determine the long-run equilibrium output and selling price for each firm
b. Determine firm A, Firm B, and total industry profits at the equilibrium solution found in Part (a).

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Solution Summary

This solution describes the steps to calculate long run equilibrium output and selling price for each of the given firms. It also calculates total industry profits.

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a. Determine the long-run equilibrium output and selling price for each firm.

In cournot competition firms compete in quantities and tend to maximize their profit
P=200-QA-QB

In case of company A
Total Revenue =TRA=P*QA=(200-QA-QB)*QA=200QA-QA^2-QAQB
Marginal Revenue=MRA=d(TRA)/dQA=200-2QA-QB

TCA=1500+55QA+QA^2
Marginal ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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